Question: The sum of two numbers is $128$, and their difference is $4$. What are the two numbers?
Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 128}$ ${x-y = 4}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 132 $ $ x = \dfrac{132}{2} $ ${x = 66}$ Now that you know ${x = 66}$ , plug it back into $ {x+y = 128}$ to find $y$ ${(66)}{ + y = 128}$ ${y = 62}$ You can also plug ${x = 66}$ into $ {x-y = 4}$ and get the same answer for $y$ ${(66)}{ - y = 4}$ ${y = 62}$ Therefore, the larger number is $66$, and the smaller number is $62$.